reserve AFV for WeakAffVect;
reserve a,b,c,d,e,f,a9,b9,c9,d9,f9,p,q,r,o,x99 for Element of AFV;

theorem Th4:
  a,b // a,c implies b = c
proof
  assume a,b // a,c;
  then a,a // b,c by Def1;
  then b,c // a,a by Th3;
  hence thesis by Def1;
end;
